On diagonal-Schur complements of block diagonally dominant matrices

It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices. (C) 2010 Elsevier Inc. All rights reserved.

Quantum critical phenomena in the XY spin chain with the Dzyaloshinski-Moriya interaction (Retracted article. See vol 80, artn 019903, 2009)

We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.

Article: Overview of Analytical Methodologies for Sea Water Analysis: Part I-Metals

A comprehensive, critical and up-to-date review of analytical methods developed during the last decade for metals present in sea water is presented. Separate sections are devoted to singular and multimetal determinations. Furthermore, a critical comparison of relative merits or demerits of a particular procedure is made in terms of sensitivity, selectivity and precision. Various aspects of analysis of sea water samples for metals are summarized, and the future trends are discussed.